1. Field of the Invention
This is a method of avoiding aliasing artifacts in the processing of CMP seismic data originating from arrays characterized by large source-receiver distances. The method is particularly useful in deep-water marine operations where the CMP gathers are made of sparsely-recorded traces.
2. Discussion of Related Art
The art of seismic exploration for natural resources is very well known. Nevertheless, a brief tutorial follows.
An acoustic source of any well-known type is caused to radiate a wavefield (fire a shot) into a body of water from a source location at or near the surface. The wavefield may be radiated by an impulsive device such as air gun, by a chirp-signal generator or by an implosive device. The acoustic radiator may be a single point-source or an array of point sources arranged in a desired pattern. Hereinafter for brevity, we will simply use the term "source".
The radiated wavefield propagates in all directions, insonifying the subsurface earth layers whence the wavefield is reflected back to the surface of the earth where the reflected wavefield is detected by an array or spread of acoustic receivers. The acoustic receivers may be of any type having a capability for converting mechanical compressional waves to electrical signals. Suitable receivers for deep water marine use include pressure sensors (hydrophones) that are responsive to stimuli from one or more spatial directions. The term "receiver" includes a single instrument or a group of several electrically-interconnected receivers arranged in a desired geometric pattern at or near the surface of the earth.
The electrical signals from the receiver(s) are delivered through data transmission means to data-conditioning and archival storage channels, one channel per receiver. The data transmission means may be electrical-wireline, optical, or ethereal in nature. Acoustic data-transmission channels are also known.
The electrical signals representative of the arrival times of reflected wavefields at the respective receivers are digitized and recorded on reproducible, computer-readable recording media such as, but not limited to, photographic time scale recordings, magnetic tapes, floppy disks, CD-ROMs or any other data-recording medium now known or as yet unknown.
The recorded data are later delivered to a processing center where the data are fed to a suitable general purpose computer of any desired type which is programmed to convert the seismic data to a visual model of the earth's subsurface. Programs in the computer include formulations and algorithms that exist for the sole purpose of operating on the digitized seismic data signals to convert those signals into a different state such as the desired visual model of a volume of the earth. The resulting model is used by geologists in recovering valuable natural resources such as oil, gas or other useful minerals for the benefit of humankind. That is, data processing algorithms exist to process the gathered seismic signals into a useful, human-interpretable format; the data are not gathered simply to provide a solution to some naked algorithm.
Geophysical surveys may be one- or multi-dimensional. In a two-dimensional survey by way of example but not by way of limitation, a source and an array including a plurality, numbering in the hundreds or perhaps thousands, of spaced-apart receivers are emplaced along a line of survey, one receiver or receiver group per data channel. The receivers, preferably separated from one another by an interval such as 25 meters, are distributed along the line of survey at increasingly greater offset distances from the source. The range in offsets may extend from about 200 meters from a source to the nearest receiver to as much as 30 kilometers or more to the most distant receiver.
With particular reference to marine exploration in deep water, a ship continuously tows a long cable containing the receivers through the water along the line of survey. A ship-borne source is fired periodically at selected time intervals followed by a listening period during which the receivers detect the returning reflected seismic wavefields. Typically the ship travels about 6 knots (about 11 km/hr). Two-way wavefield travel times of 15 seconds or more to deep earth layers are routine. Therefore, the interval between successive source firings must exceed the listening time by a comfortable margin. At the usual ship velocity of 6 knots therefore, the spatial separation between source-firing locations may be about four times the receiver spacing or about 100 meters.
FIG. 1 is a schematic drawing showing a receiver array, 8, of indefinite length, of which the first 20 receivers, represented as small circles 12.sub.0 -12.sub.20, are shown. The array is towed from left to right by a ship (not shown) and at selected intervals a source is fired at timed intervals at successive, spaced-apart source locations, shown as small inverted triangles 10.sub.0 -10.sub.4, as the spread progressively moves down the line of survey 13. As explained above the separation between a source and a receiver is the offset x.
A common mid point, such as 14, positioned on stratum 16 is acoustically illuminated by wavefields emanating from different source locations and received at different receiver locations. The first wavefield trajectory is 18, source location 10.sub.0, to receiver 12.sub.12. The next trajectory, 20, is 10.sub.1 -12.sub.16 and the third trajectory, 22, is 10.sub.2 -12.sub.20. CMP 14 is formed by summing (stacking) the three trajectories after application of the appropriate hyperbolic normal moveout to each one. Additional CMPs are generated similarly such as but not limited to CMPs 24 and 26. A three-input CMP is shown for simplicity but should not be taken as limiting. In seismic data processing, it is commonplace to achieve redundancy by CMP stacking as shown above in the time-space (t-x) domain for the purpose of canceling undesired random and coherent noise such as multiple energy. Certain types of undesired noise often only can be separated from the desired signal by transforming the data to some other domain such as the frequency-wavenumber (f-k) domain or slant stacking in tau-p (.tau.-p) space.
To avoid spatial aliasing problems it is required to have two or more samples per wavelength. But because of the lengthy listening time demanded by deep-water operations and the resulting wide separation between source locations, the in-line direction is sparsely sampled such that a single CMP in (t-x) space includes but 25% of the traces recorded per spread of each single shot as shown in FIG. 1. Temporal or spatial aliasing artifacts result which blocks the effective elimination of undesired energy such as multiples, severely distorting the desired model of the subsurface.
Winney, in U.S. Pat. No. 4,628,492, issued Dec. 9, 1986 recognized the aliasing problem in the slant stacking of seismic data. He provides a method for avoiding aliasing in .tau.-p transforms of seismic data which features identification of frequency components of the data likely to be aliased during the correlative summation steps, which components he then throws away. His method involves loss of valuable data. G. Beylkin in U.S. Pat. No. 4,760,563, issued Jul. 26, 1988, discloses a method and system for discrete transformation of measurements such as seismic data into and out of .tau.-p space which is both exact and practical in terms of processing time. The measurements can be filtered or otherwise processed in tau-p space in ways that are not practical or possible in their original space. Since the transforms into and out of tau-p space are exact, the filtered and transformed measurements are free of errors and distortions that perturb known approximate transforms which can be performed in a reasonable time. When the transformation process is carried out in frequency space it is done frequency-to-frequency, and when it is carried out in the spatial domain it can utilize a transformation matrix having a block circulant structure. In each case, the transformation process and matrix have a structure which substantially reduces storage and processing requirements as compared to known art. In real life, however, the Beylkin process turns out to be too excessively complex for routine use. Furthermore, Beyklin's method works with a single CMP at a time and therefore cannot address aliasing issues effectively.
The '563 patent is of interest because it presents a voluminous exegesis of the seismic data-processing art with respect to forward and inverse transforms between (t-x) space and the (f-k), (.tau.-p) domains. It is incorporated herein by reference for its tutorial content.
There is a need for an efficient method of processing deep-water seismic data which will provide the resolution to clearly separate undesired noise from desired signals without introducing spatial or temporal aliasing effects. It is proposed to provide a sharpening operator for improving the resolution of a CMP stack.